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Simplifying 3x2 + -9x + 13 = x2 + 2x + 5 Reorder the terms: 13 + -9x + 3x2 = x2 + 2x + 5 Reorder the terms: 13 + -9x + 3x2 = 5 + 2x + x2 Solving 13 + -9x + 3x2 = 5 + 2x + x2 Solving for variable 'x'. Reorder the terms: 13 + -5 + -9x + -2x + 3x2 + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2 Combine like terms: 13 + -5 = 8 8 + -9x + -2x + 3x2 + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2 Combine like terms: -9x + -2x = -11x 8 + -11x + 3x2 + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 8 + -11x + 2x2 = 5 + 2x + x2 + -5 + -2x + -1x2 Reorder the terms: 8 + -11x + 2x2 = 5 + -5 + 2x + -2x + x2 + -1x2 Combine like terms: 5 + -5 = 0 8 + -11x + 2x2 = 0 + 2x + -2x + x2 + -1x2 8 + -11x + 2x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 8 + -11x + 2x2 = 0 + x2 + -1x2 8 + -11x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -5.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -5.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.5x + x2 = 0 + -4 -5.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.5x + x2 = -4 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -4 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -4 + 7.5625 Combine like terms: -4 + 7.5625 = 3.5625 7.5625 + -5.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -2.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -2.75 = 1.887458609 Simplifying x + -2.75 = 1.887458609 Reorder the terms: -2.75 + x = 1.887458609 Solving -2.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.887458609 + 2.75 x = 1.887458609 + 2.75 Combine like terms: 1.887458609 + 2.75 = 4.637458609 x = 4.637458609 Simplifying x = 4.637458609Subproblem 2
x + -2.75 = -1.887458609 Simplifying x + -2.75 = -1.887458609 Reorder the terms: -2.75 + x = -1.887458609 Solving -2.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.887458609 + 2.75 x = -1.887458609 + 2.75 Combine like terms: -1.887458609 + 2.75 = 0.862541391 x = 0.862541391 Simplifying x = 0.862541391Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.637458609, 0.862541391}
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